In certain signal processing applications, it is necessary to sample data at a high rate. This is common, for instance, for isolating signals contained within a wide band. This wide band signal will often contain narrow band interferences which must be filtered out. However, because of the high sampling rate, a narrow band filter would ordinarily require an extraordinary amount of hardware. One way to reduce the amount of hardware is by reducing the sampling rate. This can be accomplished through a digital linear phase finite impulse response (FIR) filter that performs "decimation", which is a sampling rate decrease.
One type of decimation filter that has been used is the so-called Hogenauer filter, described in "An Economical Class of Digital Filters for Decimation and Interpolation", Eugene B. Hogenauer, IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-29, No. 2, April 1981, Pages 155-162. The Hogenauer filter comprises a number of cascaded integrator stages operating at a high sampling rate and a number of comb stages operating at a low sampling rate. The Hogenauer filter can bring the amount of pass band filtering or imaging error within prescribed bounds according to the number of stages in the filter. The advantage of the Hogenauer filter is that these filters require no multipliers and use limited storage and thereby lead to more economical hardware implementations. The Hogenauer filter is economical since no multipliers are required, no storage is required for filter coefficients, intermediate storage is reduced by integrating at the high sampling rate and comb filtering at the low sampling rate, compared to the equivalent implementation using cascaded FIR filters. Furthermore, the structure of the Hogenauer filters is very regular since it comprises two basic building blocks (the integrator section and the comb section). There is little external control or complicated local timing that is required. The same filter can be used for a wide range of rate change factors with the addition of a scaling circuit and a minimal changes to the filter timing.
However, a serious disadvantage of a Hogenauer filter is that the width of the pass band and the frequency characteristics outside the pass band are severely limited. In other words, a Hogenauer filter will provide only a coarse filtering of a signal.
There is a need for a digital decimation filter which filters narrow band signals that are contained in a wide band while still providing a clean frequency response and a fine filtering.